The sum (REF ) gives the exact solution of the dynamical problem. If the initial state is strongly coupled to reservoir states
(\(\Gamma \gg 1\) ), the sum contains the large number of terms oscillating with rationally independent frequencies. It is not an easy task
to identify the recurrence cycles from such a sum of the oscillating terms. To overcome the difficulty we apply the generalized Poisson summation formula introduced in [1]}, [2]}.
This method makes it possible to express the initial state amplitude \(a_s(t)\)  in terms of the recurrence cycle partial amplitudes \(a_s^{(k)}\)
\(a_s(t) = \sum _{k}a_s^{(k)}(t - 2k \pi )\,\) 
